Word Problems

Word problems test translation before they test math: rates and work, mixtures, overlapping sets, age and interest problems, and weighted averages. The arithmetic inside is rarely hard — the challenge is converting three sentences of story into equations quickly and without inventing constraints the problem never stated. Practice writing the setup in a fixed, boring format every time (define variables, one equation per fact), and learn the standard templates: rate × time = work, the two-set matrix, and the teeter-totter method for weighted averages.

Mixtures, rates, distances, ages.·Show:20 30 50

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Sub 505 (Easy)

As a salesperson, Phyllis can choose one of two methods of annual payment: either an annual salary of

35, 000 w i t hn oco mmi ss i o n or anann u a l s a l a r y o f

10,000 plus a 20 percent commission on her total annual sales. What must her total annual sales be to give her the same annual pay with either method?

Sub 505 (Easy)

Each week, a clothing salesperson receives a commission equal to 15 percent of the first

500 in s a l es an d 20 p er ce n t o f a l l a dd i t i o na l s a l es t ha tw ee k . W ha t co mmi ss i o n w o u l d t h es a l es p er so n r ece i v eo n t o t a l s a l es f or t h e w ee k o f

1,300 ?

605-655 (Medium)

The number of stamps that Kaye and Alberto had were in the ration of 5:3 respectively. After Kaye gave Alberto 10 of her stamps, the ration of the number of Kaye had to the number of Alberto had was 7:5. As a result of the gift, Kaye had how many more stamps than Alberto

505-555 (Easy)

Over the past 7 weeks, the Smith family had weekly grocery bills of

74,

69,

64,

79,

64,

84, and $77. What was the Smiths' average (arithmetic mean) weekly grocery bill over the 7-week period?

605-655 (Medium)

Each year for 4 years, a farmer increased the number of trees in a certain orchard by one fourth of the number of trees in the orchard the preceding year. If all the trees thrived and there were 6,250 trees in the orchard at the end of the 4-year period, how many trees were in the orchard at the beginning of the 4-year period?

655-705 (Hard)

At his regular hourly rate, Don had estimated the labor cost of a repair job as

336 an d h e w a s p ai d t ha t am o u n t . H o w e v er, t h e j o b t oo k 4 h o u r s l o n g er t hanh e ha d es t ima t e d an d, co n se q u e n tl y, h ee a r n e d

2 per hour less than his regular hourly rate. What was the time Don had estimated for the job, in hours?

555-605 (Medium)

On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between

Sub 505 (Easy)

David has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?

555-605 (Medium)

Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.25 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

605-655 (Medium)

A certain state's milk production was 980 million pounds in 2007 and 2.7 billion pounds in 2014. Approximately how many more million gallons of milk did the state produce in 2014 than in 2007 ?

555-605 (Medium)

Last year Brand X shoes were sold by dealers in 403 different regions worldwide, with an average (arithmetic mean) of 98 dealers per region. If last year these dealers sold an average of 2,488 pairs of Brand X shoes per dealer, which of the following is closest to the total number of pairs of Brand X shoes sold last year by the dealers worldwide?

605-655 (Medium)

When a certain tree was first planted, it was 4 feet tall and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?

Sub 505 (Easy)

A small business invests

9, 900 in e q u i p m e n tt o p r o d u ce a p r o d u c t . E a c h u ni t o f t h e p r o d u c t cos t s

0.65 to produce and is sold for $1.20. How many units of the product must be sold before the revenue received equals the total expense of production, including the initial investment in equipment?

Last Sunday a certain store sold copies of Newspaper A for

1.00 e a c han d co p i eso f N e w s p a p er B f or

1.25 each, and the store sold no other newspapers that day. If r percent of the storeâs revenues from newspaper sales was from Newspaper A and if p percent of the newspapers that the store sold were copies of newspaper A, which of the following expresses r in terms of p?

Sub 505 (Easy)

Last year

48, 000 o f a cer t ain s t or e^{'} s p r o f i tw a ss ha r e d b y i t s 2 o w n er s an d t h e i r 10 e m pl oy ees . E a c h o f t h e 2 o w n er sr ece i v e d 3 t im es a s m u c ha se a c h o f t h e i r 10 e m pl oy ees . H o w m u c h d i d e a c h o w n er r ece i v e f r o m t h e

48,000 ?

Sub 505 (Easy)

A retailer purchased eggs at

2.80 p er d oz e nan d so l d t h ee g g s a t 3 e g g s f or

0.90. What was the retailer's gross profit from purchasing and selling 5 dozen eggs?

605-655 (Medium)

Club X has more than 10 but fewer than 40 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?

605-655 (Medium)

Last year a state senate consisting of only Republican and Democrat members had 20 more Republican members than Democrat members. This year the senate has the same number of members as last year, but it has 2 fewer Republican members than last year. If this year the number of Republican members is 2/3 the number of senate members, how many members does the senate have this year?

505-555 (Easy)

The profit P, in dollars, for any given month at a certain company is defined by P= I â C, where I represents total income, in dollars, and C represents total costs, in dollars, for the month. For each of the first 4 months of the year, C = I + 32,000; and for each of the next 3 months, I = C + 36,000. If I = C + 10,000 for each of the 5 remaining months of the year, what was the company's total profit for the 12-month year?

505-555 (Easy)

If the mass of 1 cubic centimeter of a certain substance is 7.3 grams, what is the mass, in kilograms, of 1 cubic meter of this substance?

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